Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
462 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 462 conjugacy classes of subgroups — too many to draw. Only its 123 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. #24905545 | C2 | semidirect |
| 4. #24905542 | C2 | semidirect |
| 5. C83×#1376 | C2 | semidirect |
| 133. #1376 | D83 | semidirect |
| 135. C83 | #12849 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×#13050573 | 2 |
| C2×#19127482 | 2 |
| #24905545 | 2 |
| #24905542 | 2 |
| C83×#1376 | 2 |
| #12849 | 83 |